Sine, Cosine, Tangent & Cotangent of an Angle
Big Idea: Trigonometric functions connect angles to ratios of sides in a right triangle. They are among the most powerful tools in all of mathematics, used in physics, engineering, music, and beyond.
1. The Right Triangle Setup
Consider a right triangle with an acute angle $\alpha$. Relative to this angle, we label the three sides:
- Hypotenuse (c) — the side opposite the right angle (always the longest side)
- Opposite side (a) — the side directly across from angle $\alpha$
- Adjacent side (b) — the side next to angle $\alpha$ (not the hypotenuse)
Interactive visualization — available in the full lesson